Estimating Animal Abundance

by Borchers, D. L.; Buckland, S. T.; Zucchini, W.; Zucchini, W.

• ISBN13: 9781852335601
• ISBN10: 1852335602
• Format: Hardcover
• Copyright: 2004-09-27
• Publisher: Springer Verlag

Summary

This is the first book to provide an accessible comprehensive introduction to wildlife population assessment methods. It uses a new approach that makes the full range of methods accessible in a way that has not previously been possible. Traditionally, newcomers to the field have had to face the daunting prospect of grasping new concepts for almost every one of the many methods. In contrast, this book uses a single conceptual (and statistical) framework for all the methods. This makes understanding the apparently different methods easier because each can be seen to be a special case of the general framework. The approach provides a natural bridge between simple methods and recently developed methods. It also links closed population methods quite naturally with open population methods. The book is accompanied by free software on the web, in the form of an R library, allowing readers to get some "hands-on" experience with the methods and how they perform in different contexts - without the considerable effort and expense required to do this in the real world. It also provides a tool for teaching the methods, including a means for teachers to generate examples and exercises customised to the needs of their students. As the first truly up-to-date and introductory text in the field, this book should become a standard reference for students and professionals in the fields of statistics, biology and ecology.

Table of Contents

I Introduction
Introduction	3	(9)
Estimation approach 1	4	(1)
Estimation approach 2	5	(2)
Estimation approach 3	7	(1)
Heterogeneity	7	(1)
Summary	8	(1)
Outline of the book	9	(1)
R software	10	(2)
Using likelihood for estimation	12	(25)
An example problem	12	(2)
Maximum likelihood estimation	14	(5)
Known detection probability (p)	14	(1)
Unknown detection probability	14	(1)
Basics of the method	15	(1)
Likelihood function	16	(3)
Estimator uncertainty and confidence intervals	19	(5)
What are confidence intervals?	19	(3)
Constructing confidence intervals	22	(2)
Approximate confidence intervals	24	(6)
Asymptotic normality	24	(1)
Profile likelihood	25	(2)
Bootstrap	27	(3)
Summary	30	(1)
Exercises	31	(6)
II Simple Methods
Building blocks	37	(18)
State and observation models	37	(9)
State models	39	(4)
Survey design and observation models	43	(3)
Design and model	46	(7)
What is a survey design?	47	(1)
Design- vs. model-based inference	47	(2)
Can we tell if the model is wrong?	49	(2)
Design-based vs. Model-based: pros and cons	51	(1)
Relevance of design for likelihood-based inference	52	(1)
Summary	53	(2)
Plot sampling	55	(17)
Introduction	55	(1)
A simple plot survey	56	(1)
Estimation by design	57	(2)
Horvitz--Thompson estimator of abundance	57	(2)
Maximum likelihood estimation	59	(7)
Point estimation	60	(1)
Interval estimation	60	(3)
A more realistic example	63	(3)
Effect of violating assumptions	66	(1)
Summary	67	(1)
Exercises	67	(5)
Removal, catch-effort and change-in-ratio	72	(32)
Introduction	72	(2)
Removal method	74	(14)
Point estimation	74	(2)
Simple removal method MLE	76	(1)
Interval estimation	77	(6)
Heterogeneity	83	(5)
Catch-effort	88	(6)
Likelihood	90	(1)
Removal models and model selection	91	(2)
A word on CPUE as an index of abundance	93	(1)
Change-in-ratio	94	(5)
Full likelihood	96	(1)
Conditional likelihood	97	(2)
Effect of violating main assumptions	99	(1)
Summary	99	(2)
Exercises	101	(3)
Simple mark-recapture	104	(27)
Introduction	104	(2)
Single recapture and some notation	106	(2)
St Andrews data example	107	(1)
A two-sample mark-recapture likelihood	108	(8)
First capture occasion	109	(1)
Second capture occasion	109	(2)
Putting the two capture occasions together	111	(1)
Interval estimation	111	(2)
Heterogeneity	113	(3)
Related methods and models	116	(1)
Unknown marking process	116	(1)
Removal method likelihood	116	(1)
Hypergeometric models	117	(1)
Single mark, multiple captures	117	(1)
Multiple occasions: the ``Schnabel census''	117	(2)
A likelihood for multiple capture occasions	118	(1)
Capture histories and individual identification	118	(1)
Types of mark-recapture model	119	(4)
Classification by observation model	119	(2)
Models Mo, Mt, Mb, Mtb	121	(1)
Likelihoods for models Mo, Mt, Mb, Mtb	121	(2)
Examples	123	(4)
St Andrews example data revisited	123	(2)
No animal heterogeneity; true model Mt	125	(1)
No heterogeneity; true model Mt; small n	126	(1)
Effect of violating main assumptions	127	(1)
Summary	128	(1)
Exercises	128	(3)
Distance sampling	131	(34)
Introduction	131	(1)
Line transect sampling	132	(17)
A simple line transect survey	133	(4)
Maximum likelihood estimation	137	(6)
Horvitz--Thompson: estimation partly by design	143	(2)
Populations that occur in groups	145	(1)
Interval estimation	145	(2)
An example with heterogeneity	147	(2)
Point transect sampling	149	(8)
Maximum likelihood estimation	150	(4)
Horvitz--Thompson: estimation partly by design	154	(1)
Populations that occur in groups	155	(1)
Interval estimation	155	(2)
Other distance sampling methods	157	(3)
Cue counting	157	(1)
Trapping webs	158	(1)
Indirect distance sampling surveys	159	(1)
Effect of violating main assumptions	160	(1)
Summary	161	(1)
Exercises	162	(3)
Nearest neighbour arid point-to-nearest-object	165	(12)
Introduction	165	(2)
Maximum likelihood estimation	167	(1)
Interval estimation	168	(1)
Example	169	(2)
Summary	171	(1)
Exercises	172	(5)
III Advanced Methods
Further building blocks	177	(5)
Introduction	177	(1)
State models	178	(2)
Observation models	180	(2)
Spatial/temporal models with certain detection	182	(17)
Introduction	182	(2)
Temporal modelling: migration counts	184	(4)
Estimation by design	184	(1)
Maximum likelihood estimation	185	(2)
Inference with ``Unbinned'' data	187	(1)
Spatial modelling: plot sampling	188	(4)
Spatio-temporal modelling	192	(1)
Other methods	193	(3)
Summary	196	(1)
Exercises	197	(2)
Dealing with heterogeneity	199	(28)
Introduction	199	(2)
Combining state and observation models	200	(1)
Distance sampling with covariates	201	(5)
Full likelihood; animal-level variables	202	(2)
Full likelihood: survey-level variables	204	(1)
Conditional likelihood: estimation partly by design	205	(1)
Mark-recapture	206	(14)
Notation	207	(1)
Animal-level stratification	208	(1)
Unobserved heterogeneity	209	(3)
Classification of models	212	(1)
Other methods	213	(1)
Observable heterogeneity: Horvitz-Thompson and conditional likelihood	214	(1)
Observable heterogeneity: full likelihood models	215	(5)
Removal methods	220	(2)
Animal-level stratification	220	(1)
Horvitz-Thompson and conditional likelihood	221	(1)
Full likelihood methods	222	(1)
Summary	222	(1)
Exercises	223	(4)
Integrated models	227	(18)
Introduction	227	(1)
Distance sampling with a spatial model	228	(7)
Full likelihoods	228	(3)
GLM- and GAM-based methods	231	(1)
Confidence intervals	232	(1)
Example: Antarctic minke whales	232	(3)
Double-platform distance sampling	235	(5)
Full likelihood	235	(2)
Conditional likelihood	237	(2)
Example: North Sea harbour porpoise	239	(1)
Double-platform migration surveys	240	(3)
Other possibilities	243	(1)
Summary	243	(1)
Exercises	244	(1)
Dynamic and open population models	245	(24)
Introduction	246	(1)
Dynamic closed population example	247	(4)
State model	247	(2)
Observation model	249	(1)
Likelihood	250	(1)
Open population example	251	(7)
State model	252	(3)
Observation model	255	(2)
Likelihood	257	(1)
Model fitting	258	(2)
Extensions	260	(2)
A multiple-survey method example	260	(1)
Other extensions	261	(1)
Summary	262	(1)
Exercises	262	(7)
IV Overview
Which method?	269	(9)
Plot sampling	269	(2)
Removal, catch-effort and change-in-ratio	271	(1)
Mark-recapture	272	(1)
Distance sampling	273	(2)
Line transect sampling	273	(1)
Point transect sampling	274	(1)
Cue counting	274	(1)
Trapping webs	274	(1)
Indirect distance sampling surveys	275	(1)
Point-to-nearest-object and nearest neighbour methods	275	(1)
Migration counts	276	(1)
Spatial modelling and integrated models	276	(2)
A Notation and Glossary	278	(6)
Notation	278	(4)
Glossary	282	(2)
B Statistical formulation for observation models	284	(5)
Detection function	286	(1)
Multiple surveys	287	(2)
C The asymptotic variance of MLEs	289	(5)
Estimating the variance of an MLE	289	(2)
Estimating the variance of a function of an MLE	291	(1)
A one-parameter example	291	(3)
Fisher information version 1	292	(1)
Fisher information version 2	292	(1)
Observed information	292	(1)
Estimating the variance of N	293	(1)
D State models for mark-recapture and removal methods	294	(5)
Static population	294	(1)
Independent dynamics	295	(1)
Markov dynamics	296	(3)
References	299	(8)
Index	307